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Logically it would make sense that the uncertainty in the position of a proton would be higher than the uncertainty in the position of an electron because protons have more mass and are confined to the nucleus; whereas, the electron has less mass and can take a position within the atomic radius. However, I tried plugging in arbitrary values for the velocity of both particles and comparing them, but I get that the electron has less uncertainty. Can anyone demonstrate using the equation to demonstrate the idea above?
Actually, the Heisenberg equation demonstrates the opposite. Your supposition that a particle with a larger mass will have a greater certainty of position than a smaller particle traveling at the same velocity is correct. The Heisenberg equation calculates a value of uncertainty, so when dividing h/4pi by a larger number (due to the larger mass of a proton as opposed to an electron, for example) using the equation would give you a smaller number, and thus a "smaller" value of uncertainty.
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